Identifying Like Terms in the Given Expression

Oct 13, 2025 by vinooalluri.com 33 views

Understanding Like Terms

In algebra, like terms are expressions that have the same variable(s) raised to the same power. They can be added or subtracted from each other, but only if they have the same coefficient. In this article, we will focus on identifying like terms in the given algebraic expression: $\frac{2x}{5} - 5.2y + 2.2 + \frac{x}{3}$ .

What are Like Terms?

Like terms are expressions that have the same variable(s) raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. Similarly, $3y$ and $-2y$ are like terms because they both have the variable $y$ raised to the power of 1.

Identifying Like Terms in the Given Expression

To identify like terms in the given expression, we need to look for expressions that have the same variable(s) raised to the same power. Let's break down the expression into its individual terms:

$\frac{2x}{5}$
$-5.2y$
$2.2$
$\frac{x}{3}$

Analyzing Each Term

Let's analyze each term individually to see if it has any like terms.

$\frac{2x}{5}$

This term has the variable $x$ raised to the power of 1. It also has a coefficient of $\frac{2}{5}$ . We need to look for other terms that have the same variable $x$ raised to the power of 1.

$-5.2y$

This term has the variable $y$ raised to the power of 1. It also has a coefficient of $-5.2$ . We need to look for other terms that have the same variable $y$ raised to the power of 1.

$2.2$

This term has no variable. It is a constant term.

$\frac{x}{3}$

This term has the variable $x$ raised to the power of 1. It also has a coefficient of $\frac{1}{3}$ . We need to look for other terms that have the same variable $x$ raised to the power of 1.

Identifying Like Terms

Based on our analysis, we can see that there are two pairs of like terms:

$\frac{2x}{5}$ and $\frac{x}{3}$ are like terms because they both have the variable $x$ raised to the power of 1.
$-5.2y$ and $2.2$ are not like terms because they have different variables. However, $-5.2y$ and $2.2$ are not like terms because they have different variables and $2.2$ is a constant term.

Conclusion

In conclusion, the like terms in the given algebraic expression are $\frac{2x}{5}$ and $\frac{x}{3}$ . These two terms have the same variable $x$ raised to the power of 1 and can be added or subtracted from each other.

Answer

The correct answer is B. $\frac{2x}{5}$ and $\frac{x}{3}$ .

Final Thoughts

Q: What are like terms in algebra?

A: Like terms are expressions that have the same variable(s) raised to the same power. They can be added or subtracted from each other, but only if they have the same coefficient.

Q: How do I identify like terms in an algebraic expression?

A: To identify like terms, look for expressions that have the same variable(s) raised to the same power. You can also use the following steps:

Break down the expression into its individual terms.
Analyze each term to see if it has any like terms.
Look for terms that have the same variable(s) raised to the same power.

Q: What are some examples of like terms?

A: Some examples of like terms include:

$2x$ and $5x$ (both have the variable $x$ raised to the power of 1)
$3y$ and $-2y$ (both have the variable $y$ raised to the power of 1)
$\frac{2x}{5}$ and $\frac{x}{3}$ (both have the variable $x$ raised to the power of 1)

Q: What are some examples of unlike terms?

A: Some examples of unlike terms include:

$2x$ and $3y$ (have different variables)
$2x$ and $2$ (have different variables and one is a constant)
$\frac{2x}{5}$ and $2y$ (have different variables and one is a fraction)

Q: Can I add or subtract like terms?

A: Yes, you can add or subtract like terms. For example:

$2x + 3x = 5x$
$-2y - 3y = -5y$

Q: Can I add or subtract unlike terms?

A: No, you cannot add or subtract unlike terms. For example:

$2x + 3y$ cannot be simplified
$-2y + 2$ cannot be simplified

Q: Why is it important to identify like terms?

A: Identifying like terms is important because it allows you to simplify complex expressions and solve equations more easily. By combining like terms, you can make the expression more manageable and easier to work with.

Q: How do I simplify an expression by combining like terms?

A: To simplify an expression by combining like terms, follow these steps:

Identify the like terms in the expression.
Add or subtract the like terms.
Simplify the resulting expression.

For example:

$\frac{2x}{5} - 5.2y + 2.2 + \frac{x}{3}$
Identify the like terms: $\frac{2x}{5}$ and $\frac{x}{3}$
Combine the like terms: $\frac{2x}{5} + \frac{x}{3} = \frac{6x + 5x}{15} = \frac{11x}{15}$
Simplify the resulting expression: $\frac{11x}{15} - 5.2y + 2.2$

Conclusion

In conclusion, identifying like terms is an important concept in algebra. By understanding what like terms are and how to identify them, you can simplify complex expressions and solve equations more easily. Remember to always identify like terms and combine them to simplify the expression.